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- #include <algorithm>
- #include <functional>
- #include <iostream>
- #include <numeric>
- #include <string>
- #include <utility>
- #include <vector>
- using namespace std;
- struct DSU {
- vector<int> p, s;
- explicit DSU(int n) : p(n), s(n, 1) { iota(p.begin(), p.end(), 0); }
- int find(int x) { return p[x] == x ? x : p[x] = find(p[x]); }
- void unite(int a, int b) {
- a = find(a); b = find(b); if (a == b) return;
- if (s[a] < s[b]) swap(a, b); p[b] = a; s[a] += s[b];
- }
- };
- struct Edge { int u, v, w, id; };
- int main() {
- ios::sync_with_stdio(false);
- cin.tie(nullptr);
- int n, m; cin >> n >> m;
- vector<Edge> edges(m);
- for (int i = 0; i < m; ++i) {
- cin >> edges[i].u >> edges[i].v >> edges[i].w;
- --edges[i].u; --edges[i].v; edges[i].id = i;
- }
- sort(edges.begin(), edges.end(), [](const Edge &a, const Edge &b) { return a.w < b.w; });
- vector<string> answer(m, "none"); DSU dsu(n);
- for (int left = 0; left < m; ) {
- int right = left;
- while (right < m && edges[right].w == edges[left].w) ++right;
- vector<int> candidate, roots;
- for (int i = left; i < right; ++i) {
- int a = dsu.find(edges[i].u), b = dsu.find(edges[i].v);
- if (a != b) {
- candidate.push_back(i); roots.push_back(a); roots.push_back(b);
- answer[edges[i].id] = "at least one";
- }
- }
- sort(roots.begin(), roots.end()); roots.erase(unique(roots.begin(), roots.end()), roots.end());
- vector<vector<pair<int, int>>> graph(roots.size());
- for (int index : candidate) {
- int a = int(lower_bound(roots.begin(), roots.end(), dsu.find(edges[index].u)) - roots.begin());
- int b = int(lower_bound(roots.begin(), roots.end(), dsu.find(edges[index].v)) - roots.begin());
- graph[a].push_back({b, edges[index].id}); graph[b].push_back({a, edges[index].id});
- }
- vector<int> tin(roots.size(), -1), low(roots.size()); int timer = 0;
- function<void(int, int)> dfs = [&](int u, int parent_edge) {
- tin[u] = low[u] = timer++;
- for (auto [v, id] : graph[u]) {
- if (id == parent_edge) continue;
- if (tin[v] == -1) {
- dfs(v, id); low[u] = min(low[u], low[v]);
- if (low[v] > tin[u]) answer[id] = "any";
- } else low[u] = min(low[u], tin[v]);
- }
- };
- for (int v = 0; v < static_cast<int>(roots.size()); ++v) if (tin[v] == -1) dfs(v, -1);
- for (int i = left; i < right; ++i) dsu.unite(edges[i].u, edges[i].v);
- left = right;
- }
- for (const string &s : answer) cout << s << '\n';
- }
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